A circular saw takes a long time to stop rotating after the power is turned off. Without the saw blade mounted, the motor stops much more quickly. Why?

Imagine trying to push a parked car: the effort needed is much more than pushing a bicycle. That's because the car has more mass. In the world of rotation, 'moment of inertia' plays a similarly crucial role but it's not just about the amount of mass; it's also about how that mass is spread out relative to the axis of rotation.

Consider a figure skater. When they pull their arms and legs in close to their body, they spin faster. That's because they've decreased their moment of inertia by reducing the distance their mass is spread out from their spin axis. Conversely, when the skater extends their arms and legs, they slow down, as the mass is further from the axis and increases the moment of inertia.

In the case of the circular saw, mounting the blade increases the mass distribution around its spinning axis, which in turn increases its moment of inertia. This larger moment makes it harder to change the saw's rotational motion, which is why it takes longer to stop when you switch off the power.

The 'axis of rotation' is the imaginary line that an object spins around. It can be external, like the Earth rotating around the Sun, or internal, like a spinning top balancing on a point. This axis is central because the distribution of mass around it determines the moment of inertia.

In our everyday experiences with doors, we instinctively know that it takes less effort to swing open a door by pushing near the edge, far from the hinges (the axis of rotation) rather than close to them. This natural understanding hints at the principle of leverage, which is fundamentally connected to the axis of rotation.

For the circular saw, the motor shaft where the blade is mounted is the axis of rotation. When the blade is off, there's less mass distributed around this axis, so there's a lower moment of inertia, making it easier for the motor to stop its rotation.

Angular momentum might sound complex, but it's basically the rotational cousin of linear momentum, which is a product of mass and velocity for objects moving in a straight line. Angular momentum, however, depends on the rotational speed and the moment of inertia of an object spinning around an axis.

To conserve angular momentum, an ice skater spins faster when they pull their arms in; they're not adding energy from the outside, but the decrease in moment of inertia results in an increase in spinning speed to keep the momentum constant. This conservation of angular momentum is why the circular saw keeps spinning for a while after it's turned off; it has to do with maintaining the product of its rotational speed and moment of inertia.

The blade's angular momentum is high because of the higher moment of inertia and the speed at which it's rotating. When the motor turns off, there's nothing to quickly dissipate that momentum, hence the saw takes longer to come to a stop with the blade on.